Suppose you wish to predict future values of some quantity, y, using an autonomous differential equation. Experiments have been performed that give the following information: • The only equilibrium solutions are y(t) = 0, y(t) = 15, and y(t) = 60 • If the value of y is 100, the quantity decreases • If the value of y is 30, the quantity increases • If the value of y is negative, the quantity increases %3D (a) How many different phase lines match the above? Sketch all possible phase lines. (b) Provide a rough sketch of an autonomous derivative graph for each of your phase lines in part 2a. (c) For each of your different sketches in part 2b, develop a differential equation that fits the basic features.

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